The earth's magnetic field has provided a low-cost, reliable aid to navigation for many centuries. The direction of the horizontal component of the magnetic field is measurable by inexpensive instrumentation, and the derived information is used for determining horizontal bearing directions in terms of magnetic heading (i.e., azimuth angles). Among the methods proposed for guiding vehicles within traffic lanes of automated highways is the use of small permanent magnets buried in the pavement. The field patterns from the small magnets can provide a reliable navigation and signaling medium for the Intelligent Vehicle Highway System (IVHS). A concept under study uses "magnetic nails" embedded in the pavement of traffic lanes to provide reference "beacons" for guiding autonomous vehicles within the lanes and for transferring navigational information (encoded in the magnet orientations) to the vehicle and its occupants. Magnetic sensors mounted under the automotive vehicles will sense the magnetic fields produced by the embedded magnets. The system is inexpensive and reliable because the magnets require no power source and are embedded below the highway surface where they are unaffected by environmental conditions. A signal processing method must be established, however, to interpret the detected magnetic fields and to determine the orientation of each magnet and the location of the vehicle within the traffic lane (i.e., its position with respect to each magnet).
A similar problem arises in the detection and location of submarines. Airborne magnetic sensors are used for detecting the presence of submerged submarines by measuring their disturbance of the natural magnetic field. Signal processing methods used for detecting submarines are based on work done in 1949 by John E. Anderson, who showed that signals arising from the principal (dipole) field disturbance can be represented as linear combinations of three basis functions. These functions are now commonly called "Anderson functions." Methods for detecting and locating submarines from the anomalies they produce in the natural magnetic field are based on detecting and estimating the relative magnitudes of the Anderson functions in the signals. These magnitudes can then be used to estimate the location of the submarine producing the anomalies. A problem with this method is that Anderson function definitions include the time of closest approach as an unknown parameter. Estimating the time of closest approach from the signal data, however, is computationally difficult. Another problem is that the method ignores noise in the signals, and the nonlinear character of the inversion process can introduce bias errors from zero-mean noise.
Kalman filtering, a process described by R. E. Kalman in 1960, uses a feedback correction filter for estimating the state of a linear Gaussian process. Kalman filtering is statistically optimal with respect to quadratic loss functions of estimation error. Extension of the process for nonlinear problems, known as "extended Kalman filtering," uses partial derivatives of the signal with respect to unknown variables. Using this approach, the magnet location and orientation problem was solved in 1988 as a nonlinear estimation problem in which the unknown quantities are the three position components of a magnetic source (i.e., a magnetic dipole) and the three components of the dipole moment vector. Detector measurements of magnetic "signals" can be shown to be linear functions of the dipole moment vector, but nonlinear functions of the relative location of the dipole. The problem is linearized by approximating the nonlinearities with local linearities-computed as partial derivatives evaluated at the estimated dipole positions. The number of "unknowns" using extended Kalman filtering is six: three position components and three dipole moment components. Although a useful process, extended Kalman filtering is computationally complex and, in the case of magnets embedded in a highway, it does not take advantage of the a priori knowledge that there are only a finite number of discrete orientations used for the embedded magnets.
A signal processing technique known as Schweppe likelihood ratio detection was described by F. C. Schweppe in 1963. Schweppe likelihood ratio detection uses a Kalman filter for each of two contending models for a signaling process. The method computes the relative likelihood that each of the contending models is correct based on differences between the predicted and measured signals. As originally formulated by Schweppe, the method uses a fixed threshold value of the ratio of the likelihoods of the two contending models to make a decision. A trade-off between false detection rate and failure-to-detect is typically used for selecting the threshold.
An alternative approach for magnet detection based on pattern classification divides the possible conditions for the relative magnet location (i.e., with respect to the sensor) into discrete classes, such as "far on the left," "far on the right," "close on the left," "close on the right," and "right underneath." Methods of pattern analysis and classification are then used to determine which category best characterizes the signals obtained in a pass near or over a magnet. A problem with this method is that the position information is more qualitative than quantitative, thus providing poor position resolution.
For an embedded magnet subsystem, acceptable system-level performance of IVHS requires an accurate and reliable method for determining the location and orientation of embedded magnets and processing the received information in real time. The method must also exhibit robustness against unexpected signal data, such as that caused by missing magnets, anomalous noise, and accidental or deliberate spills of interfering magnetic material.